An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X be the number of months between successive payments. The cdf of X is as follows:
\( F(x)=\begin{cases}
0,\hspace{7mm} x < 1 & \quad \\
0.10, \hspace{2mm}1\leq x < 3 & \quad \\
0.40, \hspace{2mm}3 \leq x < 7 & \quad \\
0.80, \hspace{2mm} 7 \leq x < 12 & \quad \\
1,\hspace{7mm} 12 \leq x: & \quad
\end{cases} \)
(a)...